Zane's Notes

First Order Linear Recurrence Relation

Zane Fitzgerald, Oct 01, 2023

Definition

First Order Linear Recurrance Relation

Defines a relationship between two Successive terms of a sequence. Using Simultaneous Equations.

Formula of a First order linear recurrence relation

And a beginning constant value: , this constant value could also be any term in the sequence.

Types of First Order Linear Recurrence Relations

Variants of First Order Linear Recurrence Relations

Working out First Order Linear Backwards

If the equation is working out for something with or , then solve for inside of the equation.

#### *$T_4$ --> $T_3$* $$ \begin{aligned} T_4=T_{3+1}=2T_3+5=99 \\ 2T_3=94 \\ T_3=47 \end{aligned} $$
##### *$T_3$ --> $T_2$*
##### $T_2$ --> $T_1$

Working out T_1 from summed terms

We know that:

*We can then sovle for x

Given the Sequence: -3, 5, 9, 11,… Find First Order Linear Recurrence Relation Therefore, Referred to as Which can be re-written as: This is a Simultaneous Equation, therefore we can use the Elimination Method to find the value of the variables We can then rearrange b = 0.5

To Find C we can substituite it back into one of the original formulas And Re-arrange that

Now we know c=6.5 and b=0.5 Now given the master Equation:

We can substituite in our found values With a constant value of

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